SOME DYNAMICAL PROPERTIES OF THE ISING FERROMAGNET

1967 ◽  
Vol 45 (6) ◽  
pp. 2091-2111 ◽  
Author(s):  
Noboru Matsudaira
Keyword(s):  
Correlation Functions ◽  
Equations Of Motion ◽  
Pair Correlation ◽  
Linear Chain ◽  
Heat Bath ◽  
Spin Correlation ◽  
Square Lattice ◽  
Two Dimensional ◽  
The Many ◽  
Sums Of Products

Time-dependent statistics of the Ising model proposed by Glauber for the one-dimensional chain are extended to the example of a two-dimensional square lattice. Each spin is assumed to change its state through the interaction with a heat bath. The equations of motion for both the single spin and the spin correlation functions are solved approximately by using a decoupling procedure where the many-body correlation functions are taken as sums of products of pair correlation functions. As a special case, our theory allows the approximate calculation of the equilibrium properties of the system and it turns out that, in this case, our result is an improvement over the Bethe approximation. Both the frequency-dependent magnetic susceptibility and the decay of the magnetic moment to the equilibrium state are calculated above and below the Curie temperature. The fluctuation–dissipation theorem developed by Glauber for the linear chain is shown to hold in the two-dimensional case also.

Spin–Spin Correlations in Site Disordered ±J 2D Ising Spin Glasses

1998 ◽  
Vol 09 (05) ◽  
pp. 685-691
Author(s):  
B. Kawecka-Magiera ◽  
A. Z. Maksymowicz ◽  
M. Kowal ◽  
K. Kulakowski
Keyword(s):  
Correlation Functions ◽  
Spin Glasses ◽  
Interatomic Distance ◽  
Spin Correlation ◽  
Two Dimensional ◽  
Spin Correlations ◽  
Ising Spin ◽  
Bond System ◽  
Random Site

Spin–spin correlation functions <S(0)S(R)> as dependent on interatomic distance R are studied in the random-site two-dimensional Ising S=1/2 ±J system. Oscillations of the correlation functions are found, which is not a case in the random-bond system.

Critical indices for spin correlation functions in ferromagnetic films

1979 ◽  
Vol 57 (10) ◽  
pp. 1686-1698 ◽  
Author(s):  
G. Gumbs ◽  
A. Griffin
Keyword(s):  
Correlation Functions ◽  
Finite Thickness ◽  
Mean Field ◽  
Spin Correlation ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Dimensional System ◽  
Two Dimensional ◽  
Critical Indices ◽  
The Mean

Using the Ginzburg–Landau–Wilson (GLW) Hamiltonian, we obtain, with the mean-field approximation, explicit expressions for the spin–spin correlation function χ(z,z′) of a film of thickness L above the phase transition temperature Tc and the spontaneous magnetization [Formula: see text] below Tc. The boundaries are treated using a temperature-independent extrapolation length Λ. From our results, we verify explicitly that for finite L, the critical indices associated with the spin–spin correlation functions and the surface magnetization are identical with those for the analogous two-dimensional system, for both the ordinary (Λ > 0) and surface (Λ < 0) transitions. Our model results nicely exhibit the fact that as long as L is finite, when the temperature T approaches sufficiently close to Tc, there is a crossover from behaviour characteristic of a single surface to two-dimensional behaviour. Within the one-loop, Hartree self-consistent field approximation, we study the effects of mode–mode coupling on the surface layer susceptibility in films of varying thicknesses. The singular behaviour obtained in the mean-field approximation is found to be completely removed in systems of finite thickness, the susceptibilities only exhibiting a finite cusp at the transition.

TWO-DIMENSIONAL QUARTER-FILLED EXTENDED HUBBARD MODEL AT STRONG COUPLING

2005 ◽  
Vol 19 (01n03) ◽  
pp. 213-216
Author(s):  
W. F. LEE ◽  
H. Q. LIN
Keyword(s):  
Hubbard Model ◽  
Correlation Functions ◽  
Nearest Neighbor ◽  
Spin Correlation ◽  
Perturbation Approach ◽  
Effective Hamiltonian ◽  
Two Dimensional ◽  
Extended Hubbard Model ◽  
Neighbor Interaction ◽  
Electron Hopping

In this paper, we generalized the perturbation approach to study the quasi-two-dimension extended Hubbard model. This model is characterizing by intra-chain electron hopping t, on-site Column interaction U, nearest-neighbor interaction V, and inter-chain electron hopping t′ and nearest-neighbor interaction V′. An effective Hamiltonian up to sixth-order in t/U, t/V, t/V′, t′/U, t′/V and t′/V′ expansion was obtained and the spin-spin correlation functions were calculated. We presented results for t=t′, V=V′.

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